n(n-3)=5160

Solution for n(n-3)=5160 equation:

Simplifying
n(n + -3) = 5160

Reorder the terms:
n(-3 + n) = 5160
(-3 * n + n * n) = 5160
(-3n + n2) = 5160

Solving
-3n + n2 = 5160

Solving for variable 'n'.

Reorder the terms:
-5160 + -3n + n2 = 5160 + -5160

Combine like terms: 5160 + -5160 = 0
-5160 + -3n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '5160' to each side of the equation.
-5160 + -3n + 5160 + n2 = 0 + 5160

Reorder the terms:
-5160 + 5160 + -3n + n2 = 0 + 5160

Combine like terms: -5160 + 5160 = 0
0 + -3n + n2 = 0 + 5160
-3n + n2 = 0 + 5160

Combine like terms: 0 + 5160 = 5160
-3n + n2 = 5160

The n term is -3n.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3n + 2.25 + n2 = 5160 + 2.25

Reorder the terms:
2.25 + -3n + n2 = 5160 + 2.25

Combine like terms: 5160 + 2.25 = 5162.25
2.25 + -3n + n2 = 5162.25

Factor a perfect square on the left side:
(n + -1.5)(n + -1.5) = 5162.25

Calculate the square root of the right side: 71.848799572

Break this problem into two subproblems by setting 
(n + -1.5) equal to 71.848799572 and -71.848799572.

Subproblem 1
n + -1.5 = 71.848799572

Simplifying
n + -1.5 = 71.848799572

Reorder the terms:
-1.5 + n = 71.848799572

Solving
-1.5 + n = 71.848799572

Solving for variable 'n'.

Move all terms containing n to the left, all other terms to the right.

Add '1.5' to each side of the equation.
-1.5 + 1.5 + n = 71.848799572 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + n = 71.848799572 + 1.5
n = 71.848799572 + 1.5

Combine like terms: 71.848799572 + 1.5 = 73.348799572
n = 73.348799572

Simplifying
n = 73.348799572

Subproblem 2
n + -1.5 = -71.848799572

Simplifying
n + -1.5 = -71.848799572

Reorder the terms:
-1.5 + n = -71.848799572

Solving
-1.5 + n = -71.848799572

Solving for variable 'n'.

Move all terms containing n to the left, all other terms to the right.

Add '1.5' to each side of the equation.
-1.5 + 1.5 + n = -71.848799572 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + n = -71.848799572 + 1.5
n = -71.848799572 + 1.5

Combine like terms: -71.848799572 + 1.5 = -70.348799572
n = -70.348799572

Simplifying
n = -70.348799572

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {73.348799572, -70.348799572}